Moving Source Trail Pixels
Project tangent-plane motion onto a detector trail length and position angle for a supplied exposure and pixel scale.
Description
Tangent-plane motion during an exposure creates a trail with length and direction.
Tangent-plane motion during an exposure creates a trail with length and direction. East/north rates give a sky position angle, which must be transformed separately if an image uses rotated detector axes.1
Project tangent-plane motion onto a detector trail length and position angle for a supplied exposure and pixel scale.
When to use Moving Source Trail Pixels
Use this tool to project tangent-plane motion onto a detector trail length and position angle for a supplied exposure and pixel scale.
Prepare the source, detector or coordinate measurements. Confirm frame, epoch, angular units, axis directions and the stated RA proper-motion convention before entering values.
How to use Moving Source Trail Pixels and understand its results
- Prepare the source, detector or coordinate measurements. Confirm frame, epoch, angular units, axis directions and the stated RA proper-motion convention before entering values.
- Enter eastMotionArcsecPerHour, northMotionArcsecPerHour, exposureHours, pixelScaleArcsecPerPixel using the field table and calculation rules, then run the tool.
- Read trailPixels, trailAngleDegrees. The explanation below defines the units, signs, ordering and any flags or placeholder values.
- If the tool reports an input issue, correct the values and run it again. Apply the stated assumptions when interpreting a successfully returned result.
| Input field | Meaning | Value type; see rules below | Requirement |
|---|---|---|---|
| eastMotionArcsecPerHour | East motion arcsec per hour | number | Required |
| northMotionArcsecPerHour | North motion arcsec per hour | number | Required |
| exposureHours | Exposure hours | number | Required |
| pixelScaleArcsecPerPixel | Pixel scale arcsec per pixel | number | Required |
Enter signed east/north rates in arcsec/hour, nonnegative exposure hours and positive arcsec/pixel scale. Combined rate must be positive because zero motion has no defined direction. Return trail length pixels and angle east of north wrapped to [0,360); zero exposure yields zero length but retains the motion direction.
trailPixels=hypot(eastRate,northRate) × exposureHours/pixelScale Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.
| Output field | Meaning | Value type |
|---|---|---|
| trailPixels | Trail pixels | number |
| trailAngleDegrees | Trail angle degrees | number |
{
"input": {
"eastMotionArcsecPerHour": 3,
"northMotionArcsecPerHour": 4,
"exposureHours": 0.5,
"pixelScaleArcsecPerPixel": 0.1
},
"output": {
"trailPixels": 25,
"trailAngleDegrees": 36.86989764584405
}
}Limitations and assumptions
It assumes constant linear sky motion and an isotropic scale. Detector rotation, acceleration, PSF convolution and readout effects are not modeled.
Numeric inputs must be finite. Follow the calculation-specific rules for overflow, underflow and exceptional cases. Missing required fields, extra fields, wrong value types and violations of the calculation rules are input errors.
Alternative or Complementary methods
Use Shift Stack Rate Offset Grid: Plan every east/north rate-grid shift for exposures relative to a supplied time origin; linear tangent-plane motion is assumed. For a complementary task, use Parametric Trailing Loss: Evaluate an explicitly supplied quadratic trailing-loss model coefficient; this is a matched-filter SNR approximation, not an aperture-flux correction.
References
-
Moving Source Trail Pixels — tool.io
Similar or alternative tools
- Shift Stack Rate Offset Grid
Plan every east/north rate-grid shift for exposures relative to a supplied time origin; linear tangent-plane motion is assumed.
- Parametric Trailing Loss
Evaluate an explicitly supplied quadratic trailing-loss model coefficient; this is a matched-filter SNR approximation, not an aperture-flux correction.